已知函数f(x)=1+cos2x-2sin^2(x-30°).化简

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已知函数f(x)=1+cos2x-2sin^2(x-30°).化简已知函数f(x)=1+cos2x-2sin^2(x-30°).化简已知函数f(x)=1+cos2x-2sin^2(x-30°).化简f

已知函数f(x)=1+cos2x-2sin^2(x-30°).化简
已知函数f(x)=1+cos2x-2sin^2(x-30°).化简

已知函数f(x)=1+cos2x-2sin^2(x-30°).化简
f(x)=1+cos2x-2sin^2(x-30°).=cos2x+cos2(x-30)=cos2x+sin(2x+30)
=cos2x+sin2xcos30+cos2xsin30=(3cos2x)/2+(√3sin2x)/2
=√3(sin60cos2x+cos60sin2x)=√3sin(2x+60)

f(x)=1+cos2x-2sin^2(x-30°)=cos2(x-30)+cos2x=2cos(2x+2x-60)/2sin(2x-60-2x)/2=-√3cos(2x-30)
cosA+cosB=2cos((A+B)/2)sin((A-B)/2)

2cos^2

f(x)=cos2x+cos(2x-60)=cos2x+cos2xcos60-sin2xsin60=3cos2c/2-√3sin2x/2

二分之三cos2x加上二分之根号三sin2x